Self-sustained hydrodynamic oscillations in lifted jet diffusion flames: Origin and control

We use direct numerical simulation (DNS) of the Navier–Stokes equations in the low-Mach-number limit to investigate the hydrodynamic instability of a lifted jet diffusion flame. We obtain steady solutions for flames using a finite rate reaction chemistry, and perform a linear global stability analysis around these steady flames. We calculate the direct and adjoint global modes and use these to identify the regions of the flow that are responsible for causing oscillations in lifted jet diffusion flames, and to identify how passive control strategies might be used to control these oscillations. We also apply a local stability analysis to identify the instability mechanisms that are active. We find that two axisymmetric modes are responsible for the oscillations. The first is a high-frequency mode with wavemaker in the jet shear layer in the premixing zone. The second is a low-frequency mode with wavemaker in the outer part of the shear layer in the flame. We find that both of these modes are most sensitive to feedback involving perturbations to the density and axial momentum. Using the local stability analysis, we find that the high-frequency mode is caused by a resonant mode in the premixing region, and that the low-frequency mode is caused by a region of local absolute instability in the flame, not by the interaction between resonant modes, as proposed in Nichols et al. (Phys. Fluids, vol. 21, 2009, article 015110). Our linear analysis shows that passive control of the low-frequency mode may be feasible because regions up to three diameters away from the fuel jet are moderately sensitive to steady control forces.This work was funded by the European Research Council through project ALORS 2590620.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2015.29

Open-loop control of a global instability in a swirling jet by harmonic forcing: A weakly nonlinear analysis

Highly swirling flows are often prone to precessing instabilities, with an azimuthal wavenumber of m=−1. We carry out a weakly non-linear analysis to determine the response behaviour of this instability to harmonic forcing. An incompressible flow is considered, where an annular inlet provides a swirling flow into a cylindrical region. For high swirl a vortex breakdown is induced, which is found to support an m=−1 instability. By expanding about the Reynolds number where this instability first occurs, a Stuart–Landau equation for the critical mode amplitude can be found and the effect of forcing can be assessed. Two types of forcing are considered. Firstly, a Gaussian forcing confined to the inlet nozzle is used to study m=0 and m=−1 forcings. Secondly, optimal forcings (measured by the two-norm) with azimuthal wavenumbers in the range −3≤m≤3 are considered. It is found that modal stabilization is highly dependent on the azimuthal wavenumber m, which governs whether the forcing is counter or co-rotating with the direction of swirl. Counter-rotating forcings are able to stabilize the mode for a wide range of forcing frequencies, while co-rotating forcings fail to yield a stable flow. In all cases, it is the base-flow modification induced by the forced response that is the dominant underlying feature responsible for the observed stabilization. This base-flow modification seeks to reduce axial momentum near the recirculation region for co-rotating forcings, and increase it for counter-rotating forcings, thus changing the size of the recirculation bubble and producing the two distinct response behaviours.Leverhulme Trust, Isaac Newton Trus

Passive control of global instability in low-density jets

Many studies have shown that low-density jets exhibit self-excited varicose oscillations. We use direct numerical simulation of the low Mach number Navier–Stokes equations to perform a linear global stability analysis of a helium jet at the threshold of onset of these oscillations. We calculate the direct and adjoint global modes and overlap these to obtain the structural sensitivity. We find that the structural sensitivity has high magnitudes in the shear layer downstream of the entrance plane, where the flow is absolutely unstable. We use the direct and adjoint global modes to calculate the effect of a control force on the growth rate and frequency of the unstable mode. We produce maps of the regions of the flow that are most sensitive to localized open loop steady forcing in the form of a body force and a heat source. We find that the most sensitive location for open loop steady forcing is the area around the shear layer, around 2 jet diameters downstream of the exit plane, and that the influence of steady forcing and heat injection is advected by the flow outside the jet. We use these maps to calculate the influence of a ring placed in the flow. When the ring is at the same temperature as the flow, it influences the flow through its drag. The ring has most influence when placed in the inner edge of the shear layer. When the ring is heated, it also influences the flow through the density reduction caused by heat input. In this case, the ring has most influence when placed in the outer edge of the shear layer. It is also influential when placed outside the jet because the expanded gas is advected towards the jet. In both these cases, the influence of the steady change to the base flow is significantly greater than the influence of an unsteady feedback force caused by the ring

Experimental investigation of the flow in a micro-channelled combustor and its relation to flame behaviour

© 2020 Elsevier Inc. The dynamic behaviour of periodic laminar premixed acetylene-air flames in a micro-channelled combustor consisting of an array of five planar rectangular channels was found to be influenced by the equivalence ratio and flow-rate of the continuously and steadily injected premixed fuel charge. Three distinct flame stages were observed — planar, chaotic and trident, which were strongly correlated to the flow dynamics. The effect of the flow on the flame behaviour was investigated by characterizing the cold flow in a scaled-up model channel with the same aspect ratio as the combustion micro-channel. Direct flow visualization using flow tracers and quantitative velocity-field data from PIV measurements showed both an increase in the bottom recirculation zone reattachment length (along the floor of the channel) and a decrease in the lateral recirculation zone reattachment length (along the sides of the channel) with increasing flow Reynolds number. Comparison of the flow and flame transition locations downstream of the injection point suggested that the location of trident flame onset coincides with the flow bottom recirculation zone reattachment length. The planar-chaotic flame transition location was observed to be influenced by the homogeneity of the mixture downstream of the injection plane

Effect of nonlinearities on the frequency response of a round jet

We investigate the effect of nonlinearities on the frequency response of a round, incompressible jet. Experiments show that axisymmetric structures dominate the response of forced and unforced jets. In contrast, linear stability and frequency response analyses predict the asymmetric mode (m=1) to be locally more unstable and globally more amplified than the axisymmetric mode (m=0). We perform a weakly nonlinear expansion of the response of the flow to harmonic forcing and derive an asymptotic expression for the sum of this divergent series beyond its limit of validity. This expression compares reasonably well with the nonlinear gain up to forcing amplitudes an order of magnitude greater than the limit of validity of the weakly nonlinear expansion. For equal forcing amplitudes, the asymmetric mode dominates over the axisymmetric mode. This suggests that the projection of environmental forcing onto the individual azimuthal modes plays an important role in the preferred dynamics of round jets

Frequency selection mechanisms in the flow of a laminar boundary layer over a shallow cavity

© 2017 American Physical Society. We investigate the flow over shallow cavities as a representative configuration for modeling small surface irregularities in wall-bounded shear flows. Due to the globally stable nature of the flow, we perform a frequency response analysis, which shows a significant potential for the amplification of disturbance kinetic energy by harmonic forcing within a certain frequency band. Shorter and more shallow cavities exhibit less amplified responses, while energy from the base flow can be extracted predominantly from forcing that impacts the cavity head on. A structural sensitivity analysis, combined with a componentwise decomposition of the sensitivity tensor, reveals the regions of the flow that act most effectively as amplifiers. We find that the flow inside the cavity plays a negligible role, whereas boundary layer modifications immediately upstream and downstream of the cavity edges contribute significantly to the frequency response. The same regions constitute preferred locations for implementing active or passive control strategies to manipulate the frequency response of the flow

Frequency selection mechanisms in the flow of a laminar boundary layer over a shallow cavity

We investigate the flow over shallow cavities as a representa tive configuration for modelling small surface irregularities in wall-bounded shear flows. Due to t he globally stable nature of the flow, we perform a frequency response analysis, which shows a signifi cant potential for the amplification of disturbance kinetic energy by harmonic forcing within a cer tain frequency band. Shorter and more shallow cavities exhibit less amplified responses, while en ergy from the base flow can be extracted predominantly from forcing that impacts the cavity head-on . A structural sensitivity analysis, combined with a componentwise decomposition of the sensiti vity tensor, reveals the regions of the flow that act most effectively as amplifiers. We find that the fl ow inside the cavity plays a negligible role, whereas boundary layer modifications imme diately upstream and downstream of the cavity edges contribute significantly to the frequency r esponse. The same regions constitute preferred locations for implementing active or passive con trol strategies to manipulate the frequency response of the flow

Effect of nonlinearities on the frequency response of a round jet

© 2017 American Physical Society. We investigate the effect of nonlinearities on the frequency response of a round, incompressible jet. Experiments show that axisymmetric structures dominate the response of forced and unforced jets. In contrast, linear stability and frequency response analyses predict the asymmetric mode (m=1) to be locally more unstable and globally more amplified than the axisymmetric mode (m=0). We perform a weakly nonlinear expansion of the response of the flow to harmonic forcing and derive an asymptotic expression for the sum of this divergent series beyond its limit of validity. This expression compares reasonably well with the nonlinear gain up to forcing amplitudes an order of magnitude greater than the limit of validity of the weakly nonlinear expansion. For equal forcing amplitudes, the asymmetric mode dominates over the axisymmetric mode. This suggests that the projection of environmental forcing onto the individual azimuthal modes plays an important role in the preferred dynamics of round jets

A theoretical approach to the passive control of spiral vortex breakdown

Previous numerical simulations have shown that vortex breakdown starts with the formation of a steady axisymmetric bubble and that an unsteady spiralling mode then develops on top of this.We study how this spiral mode of vortex breakdown might be suppressed or promoted. We use a Lagrangian approach to identify regions of the flow which are sensitive to small open-loop steady and unsteady (harmonic) forces. We find these regions to be upstream of the vortex breakdown bubble. We investigate passive control using a small axisymmetric control ring. In this case, the steady and unsteady control forces are caused by the drag force on the control ring. We find a narrow region upstream of the bubble where the control ring will stabilise the flow and we verify this using numerical simulations. © 2012 IEEE